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With a wav file for example you can easily distinguish between bit depths


Stream #0:0: Audio: pcm_s24le ([1][0][0][0] / 0x0001), 44100 Hz, stereo, 
                    s32, 2116 kb/s


Stream #0:0: Audio: pcm_s16le ([1][0][0][0] / 0x0001), 44100 Hz, stereo,
                    s16, 1411 kb/s

However AAC seems inscrutable

Stream #0:1(und): Audio: aac (mp4a / 0x6134706D), 44100 Hz, stereo,
                         fltp, 151 kb/s
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up vote 6 down vote accepted

AAC is a lossy format (like MP3), and as Wikipedia (indeed, the same article you linked to) explains:

Technically speaking, bit depth is only meaningful when applied to pure PCM devices. Non-PCM formats, such as lossy compression systems like MP3, have bit depths that are not defined in the same sense as PCM. In lossy audio compression, where bits are allocated to other types of information, the bits actually allocated to individual samples are allowed to fluctuate within the constraints imposed by the allocation algorithm.

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